Highly sensitive asymmetric and symmetric cancer sensors with ultra-high-quality factor and resolution power

In the paper, we proposed two new highly sensitive and compact biosensors with ultra-high-quality factors based on the 1-D binary photonic crystal (silicon/air thin layer) with a defect layer. The proposed asymmetric and symmetric biosensors have just a few periods (two to five) on both sides of the defect layer and the normal cell group (INOK) and cancer cells group (YD-10B) are considered for the studies. The effects of different parameters including silicon layer thickness, air layer thickness, defect layer thickness, substrate position, number of periods, and light incident angle are considered in the biosensor operation and the biosensors are optimized based on the sensitivity. The results demonstrate that the sensitivity and defect mode wavelength of the sensors are independent of the substrate position. However, the quality factor and FOM of the sensors significantly depend on the substrate position and they are improved significantly in the symmetric sensor (~ 37% improvement in optimum condition). Also, the high sensitivities of the sensors are maintained over a wide range of silicon and air thicknesses, which is a valuable achievement in the manufacturing process. Furthermore, the sensitivity of the optimized biosensors with a defect layer thickness of 10 microns and only two periods reaches S ~ 2811 nm/RIU which is an excellent sensitivity for an optical biosensor.


Theory and method
A schematic diagram of a 1-D photonic crystal consisting of alternate silicon/air layers on a silica substrate is shown in Fig. 1. This structure can be used as an optical sensor to detect cancer cells. For this purpose, cancerous blood or saliva can be passed through all air areas or only through the middle layer of the air, so that the cancer sensor operates according to a 1-D photonic crystal without defect or with defect, respectively.
Various numerical methods such as finite difference time domain (FDTD) 29,30 , boundary element method (BEM) 31,32 , and transfer matrix method (TMM) 12 www.nature.com/scientificreports/ of the photonic crystals. Each of these methods has some advantages. For example, BEM has a very high accuracy, which is very useful in various laser and optical problems [33][34][35] . TMM is also one of the most powerful, fast, and, accurate methods for modeling periodic structures like distributed feedback (DFB) lasers, distributed Bragg reflectors (DBR), and optical sensors based on photonic crystals [36][37][38] . The transfer matrix of each layer is as follows: where β j = k 0 n j d j cos θ j = 2πn j d j cos θ j / o , j represents the layer number, d j is the thickness of the layer j , 0 is the wavelength of light in air, and θ j can be calculated using Snell-Descartes law: where n 0 = 1 and n j are the refractive index of air and the layer j , respectively. Also, θ 0 is the initial incident angle, and θ j is the incident angle in the j th layer.
The transfer matrix of m layers can be calculated by multiplying M j matrices (j = 1, 2, . . . , m) as follow: where A , B , C , and D are the matrix elements of the multilayer system. Transmission and reflection coefficients of electric amplitudes ( t and r ) and powers ( T and R ) can be calculated as follow: The transmission spectrum of perfect 1-D photonic crystals or 1-D photonic crystals without a defect layer can be exploited for sensing applications. However, this paper has no focus on these structures and is devoted to exploiting the defect modes of the proposed 1-D photonic crystals based on silicon/air layers, cancerous blood or saliva as analyte in the defect layer, and silica layer as a substrate. The silica substrate can be parallel or perpendicular to the periodic layers, which leads to passing or not passing the light through the substrate. Schematic diagrams of the proposed cancer sensors are depicted in Fig. 2. As you can observe in Fig. 2, the proposed sensors are based on a 1-D photonic crystal with a defect layer, which is located in the center of the photonic crystal, and three periods of silicon/air with an extra silicon layer are designed on both sides of the defect layer. The defect layer can be created by changing the optical properties (change the material type or refractive index) or geometrical properties (change the layer thickness) of one layer, which is almost located in the center of the structures. In fact, the proposed sensors are designed by replacing a defect layer with an air layer and changing the layer thickness. Therefore, in both proposed cancer sensors, cancerous blood or saliva are passed through the defect layer and different concentrations of cancer factors lead to the different refractive index of the defect layer and subsequently change the transmission spectrum of the structures and shift in the wavelength of the defect mode (WDM). In Fig. 2b, the position of the silica substrate is different from Fig. 2a, so that light does not pass through the substrate, which can lead to improves sensor performance. The proposed cancer sensors in Fig. 2a,b are labeled according to their substrate position as PC‖S (geometrical asymmetric configuration) and PC⊥S (geometrical symmetric configuration), respectively.  www.nature.com/scientificreports/ Various top-down and bottom-up methods are successfully employed by scientists to fabricate 1-D photonic crystals based on inorganic, organic, and inorganic/organic hybrid materials. The chemical vapor deposition (CVD) method, the physical vapor deposition (PVD) method, solving the precursor in appropriate solvents, and exploiting the spin coating or self-assembly have been established to produce PCs 28,[39][40][41][42] . Furthermore, the formation of these 1-D PC structures is possible with the electron beam lithography (EBL) method, and similar structures have already been produced and reported with this method [43][44][45] . More detailed information about experimental methods for the fabrication of 1-D photonic crystals was summarized in reference 39 .
The sensitivity, quality factor, and the figure of merit (FOM) are three important quantities, which introduce to characterize the optical sensor performance. Increasing these parameters is a measure of improving the sensor performance to detect small changes in the refractive index of the target analyte. The sensitivity of the proposed sensors can be defined as the shift of defect wavelength, r , versus the change in refractive index, n d , of the surrounding medium (cancerous blood or saliva as analyte in the defect layer) as follows.
Also, quality factor, Q, and FOM can be calculated as follows: where r and δ are the defect wavelength and the full width at half maximum (FWHM) of the defect mode.
FORTRAN and the transfer matrix method (TMM) are used to study the proposed optical cancer sensors and the results are reported in the next section. Also, it is worth mentioning that the refractive index of cancer cells can depend on various factors such as the type, size, and shape of cancer cells, the stage of cancer, and the method used to measure the refractive index. In our current study, we consider trapping a layer of cancer cells on the surface of the silicon at the boundary of the silicon-defect layer for the simulations.

Results and discussions
Transmission spectra of photonic crystal without defect (black solid line) and PC‖S (red solid line) with the layer thickness of d Si = 150 nm , d Air = 100 nm , and d d = 1200 nm are shown in Fig. 3 in the range of 250-1450 nm, to achieve a better understanding of the photonic bandgap positions and defect modes. For calculations, the average refractive index of this cancer cell group (YD-10B) is selected as the refractive index of the defect layer 46 , and the refractive index of the silicon layer, n Si ( ) , is calculated from reference 47 in the range of 250-1450 nm. Also, the refractive indices of air and silica layers are 1.00 and n SiO 2 ( = 1100nm) = 1.45 , and dispersion is neglected in the studied range for these layers. According to Fig. 3, the transmission spectrum of the 1-D photonic crystal   Fig. 3, respectively. These localized defect modes which are strongly dependent on the geometrical and optical properties of the defect layer and have high intensity and low FWHM, can be exploited for high-resolution sensing. The wavelengths of localized defect modes are shifted by changing the refractive index of the analyte in the defect layer due to the presence of cancer cells. The higher value of the shift in the resonance wavelength of the defect mode by changing the analyte refractive index leads to the greater sensitivity of the optical cancer sensor, and the sensor can sense even a low change in the refractive index of cancerous blood or saliva in the defect layer. Transmission spectra of DM 1 with four different refractive indices, from the average refractive index of healthy cells to complete cancer cells of the YD-10B cell group, are plotted in Fig. 4a to achieve a better understanding of the proposed cancer sensor operation. The results declare that replacing cancer cells with healthy cells leads to a redshift in the central wavelength of DM 1 from 1206.2 to 1224.9 nm. Also, the central wavelengths of DM 1 , DM 2 , and DM 3 modes versus the refractive index of cancerous blood are represented in Fig. 4b for the PC‖S sensor with the layer thickness of d Si = 150 nm , d Air = 100 nm , and d d = 1200 nm . The results show that increasing the refractive index causes a redshift in the central wavelength of the defect modes. The sensitivities of the PC‖S sensor for each defect mode can be obtained by fitting a linear function to each data set in Fig. 4b and it is equal to S = 522.2 nm/RIU , 328.6 nm/RIU, and 344.0 nm/RIU for DM 1 , DM 2 , and DM 3 modes, respectively.
Characteristic properties of DM 1 , DM 2 , and DM 3 in PC‖S sensors with four periods of silicon/air layers and the layer thickness of d Si = 150 nm , d Air = 100 nm , and d d = 1200 nm are calculated and gathered in Table 1 to select the appropriate defect mode for exploiting in the sensor. The refractive index of cancer cells, n d = 1.3735 , is used in the calculations of FWHM and Q factor. The sensitivities of the defect modes DM 1 , DM 2 , and DM 3 are 522.2, 328.6, and 344.0 nm/RIU, respectively. According to the collected results in Table 1, an increase in the sensitivity and FWHM is observed with an increase in the central wavelength of the defect mode from DM 3 to DM 1 , while the quality factor and FOM have a decreasing trend. As you can observe, the quality factor and FOM of DM 1 are high enough for experimental work and the sensitivity of this mode for detecting cancer cells is more than DM 2 and DM 3 which means that DM 1 is suitable for exploiting in the proposed cancer sensor. In addition, DM 2 is not suitable due to its vicinity to the edge of the photonic gap, which limits the operation range of the sensor. Furthermore, the absorption of the cells at DM 1 wavelength is significantly lower than DM 2 and DM 3 wavelength 48 , which is another important reason for exploiting DM 1 for cancer cell sensing. Therefore, DM 1 is selected for the following calculations, and geometrical optimization of the proposed optical cancer sensors is done based on the defect mode.
The effect of air and silicon layer thickness. In Fig. 5a, the central wavelength of DM 1 and the sensitivity of the proposed sensors versus the thickness of the air layer are plotted. The results declare that there is no significant difference in the sensitivity and central wavelength of DM 1 in PC‖S and PC⊥S sensors, and these quantities can be considered equal in these two proposed sensors with a good approximation. Also, the DM 1 wavelength experiences a redshift from 1219.6 to 1286.8 nm and the sensitivity shows a decreasing trend with increasing air thickness from 100 to 300 nm. Also, in www.nature.com/scientificreports/ indicates the existence of the same optimal geometric structure based on sensitivity for PC‖S and PC⊥S sensors. Also, the central wavelength of DM 1 experiences a redshift from 1038.0 to 1255.8 nm with increasing the silicon thickness from 70 to 160 nm. Therefore, according to Fig. 5a,b, the central wavelengths of DM 1 in both sensors depend on the thickness of a period, d Air + d Si , in the proposed sensors, and also increasing the thickness of each layer in a period can lead to an increase in the wavelength of the defect mode. Also, the sensitivity dependences on the air and silicon layer thicknesses are different in Fig. 5a,b, and also the results demonstrate that the thickness of the air and silicon layers are two important geometric quantities in the sensor operations and they should be carefully optimized to obtain the most sensitive sensors. Now, the thicknesses of the air and silicon layers are changed simultaneously and the sensitivities of the PC‖S sensors are shown in Fig. 6b to obtain the optimum condition. Also, the calculated wavelengths of DM 1 by simultaneously changing these two thicknesses are presented in Fig. 6a. According to the results, the wavelengths  www.nature.com/scientificreports/ of DM 1 depend on the thickness of a period, d Air + d Si , in the sensor and it experiences a redshift with increasing the thickness of every layer in a period. Also, increasing the thickness of silicon and air layers from 70 to 160 nm and 100 to 300 nm leads to a change in the wavelength of DM 1 in the range of 1038 to 1332 nm, which is a significant change. Indeed, the results of Fig. 6b demonstrate that the maximum sensitivity of the PC‖S sensor (and PC⊥S sensor with a good approximation) is achieved in the range of air thickness d Air = 200 − 300 nm and silicon thickness d si = 80 − 100 nm . Furthermore, the high sensitivity of the sensor (about 682 nm/RIU ) is maintained over a wide range of silicon and air thicknesses. Therefore, Fig. 6a,b provide unique information for researchers and industrial owners about the appropriate thicknesses of silicon and air layers depending on the required wavelength range, and required sensor sensitivity. Also, it should be mentioned that maintaining high sensitivity over a wide range of silicon and air layer thicknesses convinces the manufacturers that small changes in the layer thicknesses during the manufacturing process lead to no significant drop in the sensitivity and performance of the proposed sensors, which is an important advantage in the manufacturing process of the sensors. Up to now, the proposed structures were optimized based on sensitivity. However, some important quantities like FWHM, quality factor, and FOM also should be carefully investigated during the optimization process. These main characteristic parameters of the sensors are calculated for different thicknesses of the silicon and air layers and the results are presented in Table 2. According to the results, the quality factor and FOM are also significantly improved during the optimization of sensors based on sensitivity in Fig. 6b. The highest sensitivity, quality factor, and FOM of the proposed sensors are obtained in silicon and air thicknesses d Si = 89 nm , d Air = 275 nm , which are presented in the last two rows of Table 2. Therefore, during the optimization process based on sensitivity, other important quantities of the sensors are improved and these thicknesses can be introduced as the optimum geometrical conditions to achieve high-performance operation in the proposed sensors.
In addition, another significant result in Table 2 is related to FWHM, quality factor, and FOM of the defect mode in the two proposed sensors. Although the sensitivity and DM 1  www.nature.com/scientificreports/ respectively, which are desirable values compared to other reported sensors. This phenomenon can be understood by the high reflection (HR) resonator created by DBR on both sides of the defect layer which leads to the high confinement of the electromagnetic wave in the defect layer or analyte section. The confinement causes to increase in the photon lifetime and quality factor of the structures. Also, it leads to increasing the interaction of light with the target analyte and consequently increasing the sensitivity and FOM. Also, it should be mentioned that these values are much better in the PC⊥S sensor, and they are improved to 22% compared to in PC‖S sensor in optimum condition. The improvement is due to the change of substrate position in the PC⊥S configuration that, unlike the PC‖S sensor, light does not pass through the silica substrate. Another important point of the proposed sensors is the high sensitivity, high-quality factor, and excellent FOM obtained in optimum geometrical conditions with only four periods on both sides of the defect layer, which is a low number of periods. It leads to reducing the size of the sensors significantly, making simplicity in the manufacturing process, and proposing them as an excellent candidate for use in compact sensors.
The Effect of period numbers. The number of periods (2, 3, 4, and 5 periods) on both sides of the defect layer is changed and the thickness of silicon and air layers in the proposed sensors are optimized based on the sensitivity to investigate the effect of period number on the sensor's operations. In the calculations, the thickness and refractive index of the defect layer are set on d d = 1200 nm and n d = 1.3735 (average refractive index of YD-10B cells group), respectively. The characteristic parameters of the proposed cancer sensors with different period numbers in optimum structures were calculated and the results are presented in Table 3. According to the results, the optimum sensors with different period numbers have approximately the same thicknesses of silicon and air layers. Also, the same DM 1 wavelength and sensitivity are obtained in optimized sensors, especially after using two periods. Therefore, the sensitivity of the proposed sensors is well independent of the number of periods in the studied range. However, increasing the periods on both sides of the defect layer significantly increases the quality factor and FOM that reach up to 6,212,806 and 3,783,911, respectively, in PC⊥S with five periods. The increasing trend can be understood by increasing the reflectance of DBRs as a result of an increase in the number of periods.  Table 3, the quality factor and FOM of the proposed sensors with four periods on both sides of the defect layer ( N = 4 ) are high enough, so subsequent research is focused on these structures to reach an optimum sensor with easier production than five periods.
The effect of defect layer thickness. The thickness of the defect layer is another factor that can affect the operation of the proposed cancer sensors. However, in previous calculations, it was set at 1200 nm. In this section, the optimized cancer sensors PC‖S and PC⊥S with four periods on both sides of the defect layer are selected and the thickness of the defect layer is changed in the range of 1100 to 1200 nm to investigate the effect of the defect layer thickness on the sensor's operations including central wavelength, sensitivity, quality factor, and FOM. The calculated central wavelength and sensitivity of the proposed sensors are shown in Fig. 7a. As you can observe, the sensitivity and DM 1 wavelength of both sensors at different thicknesses of the defect layer are equal. Also, an increasing trend in the DM 1 wavelength and sensitivity is observed with increasing the thickness of the defect layer. Also, the thickness of the defect layer is increased from 1.2 to 1.63 μm to investigate the  www.nature.com/scientificreports/ effect of further increasing the thickness on sensitivity. The results declare that this increase leads to improving sensitivity from 681.1 to 855.1 nm/RIU, which means the sensitivity of the structure can be further increased with more increase in the defect layer thickness. This increasing trend of sensitivity with the defect layer thickness is consistent with other reported studies on cancer sensors based on 1-D PC 23 and can be due to increasing the interaction of light with the target analyte infiltrated in the defect layer and consequently more change in the DM 1 wavelength with a given change in the refractive index of the analyte. Also, the quality factor and FOM of the sensors are plotted versus the thickness of the defect layer in Fig. 7b. The results demonstrate that increasing the thickness of the defect layer in both proposed sensors leads to an increase in the quality factor and FOM significantly. This increase can be due to increasing light and cancer cell interaction because of increasing the thickness of the defect layer. Furthermore, the quality factor and FOM of the PC⊥S sensor are remarkably better than the PC‖S sensor due to the substrate position and direction of light propagation. Therefore, increasing the thickness of the defect layer leads to improvement in the sensor operation.
The effect of light incident angle. The results of the previous section demonstrate that sensitivity rises with increasing the thickness of the defect layer. The light incident angle also can be another effective quantity on sensor operation that should be considered. The light incident angle is changed in the range of 0° to 89° degrees and calculated DM 1 wavelength and sensitivity are plotted in Fig. 8. According to the results, the DM 1 wavelength and sensitivity depend on the light incident angle significantly, and a decreasing/ increasing trend in the DM 1 wavelength/ sensitivity is observed with increasing the light incident angle. The DM 1 wavelength of the proposed sensor decreases from 1445.7 to 1030.4 nm and the sensitivity increases from 855.1 to 1415.8 nm/RIU (up to 65% improvement) by increasing the light incident angle from 0° to 89°, which is a significant improvement in the sensor operations. This improvement with increasing the incident angle is consistent with the other reported sensors based on 1-D PC 23,49 .
The reason for the phenomena can be explained as follows: increasing the incident angle leads to an increase in the effective thickness of the defect layer followed by an increase in the light and analyte interaction. Therefore, the sensitivity of the biosensor is improved by increasing the incident angle.
It is also worth mentioning that a high-sensitivity sensor with a small period number, even up to two periods on both sides of the defect layer, can be available by applying the light in incident angles around 89°. As depicted www.nature.com/scientificreports/ in Fig. 9, the sensitivity, quality factor, and FOM of the PC⊥S sensor with the given layer thicknesses of Fig. 8, the light incident angles of 89°, and only two periods on both sides of the defect layer are 1415.8 nm/RIU, 2,453,346, and 3,371,058, respectively, which are desirable values. Therefore, if there are enough facilities to apply light in high incident angles, really small sensors with a small number of periods (only two periods on both sides of the defect layer) can be produced to provide a highly sensitive sensor with lower practical limitations and smaller size for using in a compact multifunctional sensing device. As mentioned, obtaining a low number of periods and a small highly sensitive sensor with ultra-quality factor is possible in the high incident angles. Applying the incident angle of 89° leads to the best result, but it also leads to production difficulty too. Also, the difference in the sensitivities of the sensors with the incident angles of 89° and 85° is very small (less than 6 nm/RIU), therefore, the incident angle of 85° is selected for the following investigations.
The results declare that operation parameters of the sensors including sensitivity experience a significant improvement by increasing the thickness of the defect layer and the thickness in some reported 1-D PC sensor sets at 13 times the thickness of each period 2,23 . Therefore, the thickness of the defect layer is increased up to d d = 10µm , and then the biosensor is optimized based on sensitivity at the selected incident angle. The sensitivity of the optimized biosensor ( d Si = 179 nm , d Air = 703 nm ) increases and reaches S = 2810.7 nm/RIU , which is a valuable achievement. The results of the currently reported sensors along with the current work are gathered in Table 4 to compare them. As you can observe, the proposed asymmetric and symmetric biosensors have high sensitivity and Q factor and they can be considered as a very worthy candidate for biosensing.

Conclusion
We proposed two new portable highly sensitive and compact biosensors with ultra-high-quality factors to achieve the rapid and real-time detection of cancer cell groups. The proposed refractive index biosensors were designed based on a 1-D binary photonic crystal (silicon/air thin layer) with a defect layer (cancerous blood or saliva) to sense the low concentrations of cancer cells. The normal cell group (INOK) and cancer cell group (YD-10B) were selected for investigation. The shift of a defect mode wavelength located in the IR region with the presence of cancer cells was exploited to sense cancer cells. In the first step of studies, the order of periodic layer and defect layer thicknesses was selected with a study of the previously successful theoretical and experimental 1-D PC sensors with different materials published in scientific literature and also our previously published research in reference 12 and a sensitivity S = 522.2 nm/RIU was achieved for the normal incident to our proposed sensors with a typical thickness of d Si = 150 nm , d Air = 100 nm , and d d = 1200 nm . In the second step, different parameters including the thickness of layers, the number of periods, and the incident angle were changed to achieve the optimized biosensor with the highest sensitivity, and the sensitivity of the biosensors raises and reaches S = 2810.7nm/RIU in the optimum condition ( d Si = 179 nm , d Air = 703 nm ), which is a valuable achievement. Therefore, it is worth mentioning that the optimized parameters of our proposed sensors (final values) are completely independent of the initial values. Furthermore, high sensitivity is maintained over a considerable range of silicon and air thicknesses, and excellent sensor performances are provided using a low number of periods, which can convince everyone that the small changes in the layer thicknesses during the manufacturing process lead to no significant drop in sensitivity and performance of the proposed cancer sensors. Table 4. Comparison of the sensitivity and quality factor of recently published optical biosensors along with the proposed sensors in current work.